Properties

Label 1134.2.l
Level $1134$
Weight $2$
Character orbit 1134.l
Rep. character $\chi_{1134}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $8$
Sturm bound $432$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(432\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

Total New Old
Modular forms 480 64 416
Cusp forms 384 64 320
Eisenstein series 96 0 96

Trace form

\( 64q - 64q^{4} - 10q^{7} + O(q^{10}) \) \( 64q - 64q^{4} - 10q^{7} - 30q^{13} + 64q^{16} - 32q^{25} + 10q^{28} + 10q^{37} + 10q^{43} - 12q^{46} + 22q^{49} + 30q^{52} - 30q^{58} - 64q^{64} - 4q^{67} + 54q^{70} - 88q^{79} + 24q^{85} - 12q^{91} - 30q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1134.2.l.a \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+(-2\zeta_{12}-2\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.b \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q+\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.c \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.d \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}^{3}q^{2}-q^{4}+(3-2\zeta_{12}^{2})q^{7}+\cdots\)
1134.2.l.e \(8\) \(9.055\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6})q^{5}+\cdots\)
1134.2.l.f \(8\) \(9.055\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}-2\zeta_{24}^{3}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1134.2.l.g \(16\) \(9.055\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+(\beta _{4}+\beta _{9})q^{2}-q^{4}+(\beta _{1}+\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots\)
1134.2.l.h \(16\) \(9.055\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{4}-\beta _{9})q^{2}-q^{4}+(-\beta _{1}-\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)